There are 26 letters, so the total number of strings of 4 lowercase letters is

\(\displaystyle{26}^{{4}}={456},{975}\)

(in each of the four places, we can put any of the 26 letters).

On the other hand, the number of strings of 4 lowercase letters that do not have the letter x in them is

\(\displaystyle{25}^{{4}}={390},{625}\)

(in each of the four places, we can put any of the 25 letters, since we are excluding x).

Finally, the difference of these numbers is the number of strings of 4 lowercase letters that have the letter x in them:

\(\displaystyle{26}^{{4}}-{25}^{{4}}—{456.975}—{390},{625}={66},{350}\)

\(\displaystyle{26}^{{4}}={456},{975}\)

(in each of the four places, we can put any of the 26 letters).

On the other hand, the number of strings of 4 lowercase letters that do not have the letter x in them is

\(\displaystyle{25}^{{4}}={390},{625}\)

(in each of the four places, we can put any of the 25 letters, since we are excluding x).

Finally, the difference of these numbers is the number of strings of 4 lowercase letters that have the letter x in them:

\(\displaystyle{26}^{{4}}-{25}^{{4}}—{456.975}—{390},{625}={66},{350}\)